Non-Uniform Norm Constraint LMS Algorithm for Sparse System Identification

Sparsity property has long been exploited to improve the performance of least mean square (LMS) based identification of sparse systems, in the form of l₀-norm or l₁-norm constraint. However, there is a lack of theoretical investigations regarding the optimum norm constraint for specific system with different sparsity. This paper presents an approach by seeking the tradeoff between the sparsity exploitation effect of norm constraint and the estimation bias it produces, from which a novel algorithm is derived to modify the cost function of classic LMS algorithm with a non-uniform norm (p-norm like) penalty. This modification is equivalent to impose a sequence of l₀-norm or l₁-norm zero attraction elements on the iteration according to the relative value of each filter coefficient among all the entries. The superiorities of the proposed method including improved convergence rate as well as better tolerance upon different sparsity are demonstrated by numerical simulations.